“By Deputy”


As Shakespeare couldn’t write his plays
(If Mrs. Gallup’s not mistaken),
I think how wise in many ways
He was to have them done by Bacon;
They might have moldered on the shelf,
Mere minor dramas (and he knew it!),
If he had written them himself
Instead of letting Bacon do it.

And if it’s true, as Brown and Smith
In many learned tomes have stated,
That Homer was an idle myth,
He ought to be congratulated,
Since thus, evading birth, he rose
For men to worship at a distance;
He might have penned inferior prose
Had he achieved a real existence.

To him and Shakespeare men agree
In making very nice allusions;
But no one thinks of praising me,
For I compose my own effusions;
As others wrote their works divine
And they immortal thus today are,
Perhaps had someone written mine
I might have been as great as they are.

— Arthur St. John Adcock

The Asymmetric Propeller

asymmetric propeller theorem

Arrange three congruent equilateral triangles so that their corners meet at a point, like the red triangles above. The arrangement doesn’t have to be symmetric; the triangles can even overlap. Now draw lines BC, DE, and FA to complete a hexagon inscribed in a circle. The midpoints of these three lines will form the vertices of an equilateral triangle.

That’s called the asymmetric propeller theorem, and it’s been known since the 1930s. But in 1979 Beverly Hills dentist and geometry enthusiast Leon Bankoff told Martin Gardner of some further discoveries. Bankoff never found time to write them up, so after the dentist’s death in 1997 Gardner published them in the College Mathematics Journal:

  • The three equilateral triangles need not be congruent. Each can be of any size and the theorem still holds.
  • The triangles need not meet at a point. They can meet at the corners of any equilateral triangle.
  • They need not even be equilateral! If three similar triangles of any sizes meet at a point, the midpoints of the three added lines will form a triangle similar to each of the “propellers.”
  • The similar triangles need not meet at a point! If they meet at the corners of a fourth triangle (of any size) that’s similar to each propeller, then the midpoints of the added lines will form a triangle similar to each propeller, provided that the vertices of the central triangle touch the corresponding corners of the propellers.

Given all this flexibility, Gardner asked, do the propellers even have to be triangles? It turns out that the answer is yes. Still, the discoveries above form a fitting tribute to Bankoff, whom Gardner called “one of the most remarkable mathematicians I have been privileged to know.”

(Martin Gardner, “The Asymmetric Propeller,” College Mathematics Journal 30:1 [January 1999], 18-22.)

The Uncounted


It was a good answer that was made by one who when they showed him hanging in a temple a picture of those who had paid their vows as having escaped shipwreck, and would have him say whether he did not now acknowledge the power of the gods, — ‘Aye,’ asked he again, ‘but where are they painted that were drowned after their vows?’ And such is the way of all superstition, whether in astrology, dreams, omens, divine judgments, or the like; wherein men, having a delight in such vanities, mark the events where they are fulfilled, but where they fail, though this happens much oftener, neglect and pass them by.

— Francis Bacon, Novum Organum, 1620

In a Word

n. intellectual or social pretension or affectation; pseudo-intellectual speech, writing, debate, etc.

adj. pretentiously or affectedly literary

n. a learned fool



Raymond Chandler’s 10 rules for writing a detective novel:

  1. It must be credibly motivated, both as to the original situation and the dénouement.
  2. It must be technically sound as to the methods of murder and detection.
  3. It must be realistic in character, setting and atmosphere. It must be about real people in a real world.
  4. It must have a sound story value apart from the mystery element: i.e., the investigation itself must be an adventure worth reading.
  5. It must have enough essential simplicity to be explained easily when the time comes.
  6. It must baffle a reasonably intelligent reader.
  7. The solution must seem inevitable once revealed.
  8. It must not try to do everything at once. If it is a puzzle story operating in a rather cool, reasonable atmosphere, it cannot also be a violent adventure or a passionate romance.
  9. It must punish the criminal in one way or another, not necessarily by operation of the law. … If the detective fails to resolve the consequences of the crime, the story is an unresolved chord and leaves irritation behind it.
  10. It must be honest with the reader.

That’s from Chandler’s notebooks. As it happens, Dashiell Hammett, Ronald Knox, and S.S. Van Dine all came up with similar lists. Mystery writers must be very methodical people.

Parrondo’s Paradox


Imagine a staircase with 1001 stairs, numbered -500 to 500. You’re standing in the middle, on stair 0, and you want to reach the top. On each step you can play either of two coin-flipping games — if the result is heads then you move up a step; if it’s tails then you move down a step:

  • In game 1 you flip coin A, which is slightly biased: It comes up heads 49.5 percent of the time and tails 50.5 percent.
  • In game 2 you use two coins, B and C. Coin B produces heads 9.5 percent of the time and tails 90.5 percent. Coin C produces heads 74.5 percent of the time and tails 25.5 percent. In game 2 if the number of the stair you’re on is a multiple of 3 then you flip coin B; otherwise you flip coin C.

Both of these are losing games — if you played either game 1 or game 2 exclusively, you’d eventually find yourself at the bottom of the staircase. But in 1996 Spanish physicist Juan Parrondo found that if you play the two games in succession in random order, keeping your place on the staircase as you switch between them, you’ll rise to the top of the staircase. It’s not, properly speaking, a paradox, but it’s certainly counterintuitive.

This example is from David Darling’s Universal Book of Mathematics. (Thanks, Nick.)

“What’ll Be the Title?”


O to scuttle from the battle and to settle on an atoll far from brutal mortal neath a wattle portal!
To keep little mottled cattle and to whittle down one’s chattels and not hurtle after brittle yellow metal!
To listen, non-committal, to the anecdotal local tittle-tattle on a settle round the kettle,
Never startled by a rattle more than betel-nuts a-prattle or the myrtle-petals’ subtle throttled chortle!
But I’ll bet that what’ll happen if you footle round an atoll is you’ll get in rotten fettle living totally on turtle, nettles, cuttle-fish or beetles, victuals fatal to the natal élan-vital,
And hit the bottle.
I guess I’d settle
For somewhere ethical and practical like Bootle.

— Justin Richardson

Arms Race


Fly-plagued and enterprising in 1919, G.W. Blake came up with this inventive solution. The spring-loaded pistol shoots a projectile bearing a woven wire screen fast enough to surprise an unwitting fly who might have been expecting a low-tech flyswatter.

Next I suppose the flies will start shooting us.

A Disturbing Dinner

When British traveler Richard Gordon Smith reached Japan’s Lake Biwa in 1906, he asked a local cook whether he could prepare the rare dish koi-no-ikizukuri (“a carp cut up alive”), which had been offered at nobles’ feasts in ancient times. The cook, delighted, brought in a red lacquered tray decorated to resemble the sea bottom. On it lay a carp that opened and shut its mouth and gills as if it were swimming in water. “The dish was really pretty in spite of the gasping fish which, however, showed no pain, and there was not a sign of blood or a cut.” But “Now we are ready,” said the cook, and he dribbled some soy sauce into the fish’s eye:

The effect was not instantaneous: it took a full two minutes as the cook sat over him, chopsticks in hand. All of a sudden and to my unutterable astonishment, the fish gave a convulsive gasp, flicked its tail and flung the whole of its skin on one side of its body over, exposing the underneath of the stomach parts, skinned; the back was cut into pieces about an inch square and a quarter of an inch thick, ready for pulling out and eating.

“Never in my life have I seen a more barbarous or cruel thing,” Smith wrote, “not even the scenes at Spanish bull fights. Egawa [his interpreter] is a delicate-stomached person and as he could eat none, neither could I. It would be simply like taking bites out of a large live fish. I took the knife from my belt and immediately separated the fish’s neck vertebrae, much to the cook’s astonishment and perhaps disgust.” He asked them to take it away. “You have certainly operated beautifully,” he said, “but the sooner a law is brought in to prevent such cruelty the better.”

(From Travels in the Land of the Gods: The Japan Diaries of Richard Gordon Smith, 1986.)